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Jones, Peter W.

Quasiconformal mappings and extendability of functions in Sobolev spaces. (English) Zbl 0489.30017

Acta Math. 147, 71-88 (1981).
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Cited in 15 Reviews
Cited in 295 Documents

MSC:

30C62 Quasiconformal mappings in the complex plane
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Keywords:

Sobolev spaces; quasiconformal mappings; extension operator; quasisphere; (epsilon, delta)-domains

Citations:

Zbl 0416.30014; Zbl 0474.46020
Cite Review PDF
Full Text: DOI

References:

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[10] – Hausdorff dimension and quasiconrormal mappings,J. London Math. Soc., 6 (1973), 504–512. · Zbl 0258.30020 · doi:10.1112/jlms/s2-6.3.504
[11] Gol’dshtein, V. M., Latfullin, T. G. &Vodop’yanov, S. K., Criteria for extension of functions of the classL 2 1 from unbounded plain domains.Siberian Math. J. (English translation), 20: 2 (1979), 298–301. · Zbl 0436.30013 · doi:10.1007/BF00970040
[12] Gol’dhtein, V. M., Reshetnyak, Yu. G. &Vodop’yanov, S. K., On geometric properties of functions with generalized first derivatives.Uspehi Mat. Nauk., 34: 1 (1979), 17–65. English translation inRussian Math. Surveys, 34: 1 (1979), 19–74.
[13] Hestenes, M., Extension of the range of a differentiable function.Duke Math. J., 8 (1941), 183–192. · Zbl 0024.38602 · doi:10.1215/S0012-7094-41-00812-8
[14] Jerison, D. & Kenig, C., Boundary behavior of harmonic functions in nontagentially accessible domains. Preprint. · Zbl 0514.31003
[15] Jones, P. W., Extension theorems for BMO.Indiana Math. J., 29 (1980), 41–66. · Zbl 0432.42017 · doi:10.1512/iumj.1980.29.29005
[16] Lehto, O. &Virtanen, K. I.,Quasiconformal mappings in the plane. 2nd ed., Springer-Verlag, New York, 1973. · Zbl 0267.30016
[17] Lichtenstein, L., Eine elementare Bemerkung zur reelen Analysis.Math. Z., 30 (1919). · JFM 47.0456.01
[18] Martio, O. & Sarvas, J., Injectivity theorems in the plane and space.Ann. Ann. Acad. Sci. Fenn. To appear. · Zbl 0406.30013
[19] Mostow, G. D., Quasiconformal mappings inn-space and the rigidity of hyperbolic space forms.I.H.E.S. Publ. Math., 34 (1968), 53–104. · Zbl 0189.09402
[20] Stein, E. M.,Singular integrals and differentiability properties of functions. Princeton University Press, Princeton. New Jersey, 1970. · Zbl 0207.13501
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